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The radius of the earth is supposed to be 6300 km and the distance of the moon from the earth being 60 times the radius of the earth, find approximately the radius of the moon which subtends at the earth an angle of 21'.
solve this problem step by step .....​

Sagot :

sqdancefan

9514 1404 393

Answer:

  1155 km

Step-by-step explanation:

The arc length of the moon's diameter is ...

  s = rθ . . . . . where r is the distance to the moon, θ is the subtended arc in radians, and s is the moon's diameter.

There are 180° in π radians, and there are 60' in 1°. That means there are π/10800 radians in each minute of arc.

  s = (60·6300 km)(21/10800π) = 2309 km

The radius of the moon is estimated to be half this diameter, or ...

  moon radius ≈ 1155 km

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Additional comment

We have calculated the radius of the moon based on the numbers given in this problem. The angle subtended by the moon is actually about 31', not 21'.

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